Though there were no traditional exit polls, Brown’s 5-percentage-point victory in a state where just 12 percent of registered voters are Republicans makes clear that yet again, Democrats lost a race on friendly terrain because centrists fled into the arms of the GOP.

As they did in the New Jersey and Virginia gubernatorial contests last fall, sour swing voters overwhelmingly supported the Republican in Tuesday’s Massachusetts Senate special election. Though there were no traditional exit polls, Brown’s 5-percentage-point victory in a state where just 12 percent of registered voters are Republicans makes clear that yet again, Democrats lost a race on friendly terrain because centrists fled into the arms of the GOP.

After Barack Obama won independents by 52 percent to 44 percent in 2008, the key demographic in American politics is moving away from him and his party. And as in any 12-step program to recovery, Democratic officials are finally owning up to having a problem with the swing bloc.

Though there were no exit polls, GOP pollster Tony Fabrizio surveyed 800 voters on election night and found that Brown won 64 percent of independents to Coakley’s 34 percent.

Democratic pollster Dave Beattie said that independent voters — particularly whites and Hispanics — are worried about the economy and that Democrats had erred in focusing on health care at a time when voters are focused on jobs.

“These are the same individuals that ditched the Republicans in the last couple of elections,” Beattie lamented. “These are folks who don’t like the way things are going.”

After the corporate bailouts, middle-class voters felt particularly neglected, he said. “It’s a feeling that the whole system in Washington is ignoring them,” Beattie said. “We have not addressed the economic concern.”

But the cure for Democrats isn’t as simple as tweaking their agenda, it would appear. Donahue, a nurse, complained about the federal health care reform plans and said one-party control in Washington was partially to blame. “We need a little bit of diversity politically,” she said.

The Bay State’s results proved that she is not alone.

A survey taken by GOP pollster Wes Anderson for the Republican National Committee in the days leading up to the Massachusetts vote found deep discontent with the Democratic majority in Congress in a state that, until Tuesday, didn’t have a single Republican on Capitol Hill.

Asked whether they were satisfied that Democrats in Congress were listening to them, 67 percent of Massachusetts independents polled said they were unsatisfied compared with just 28 percent who said they were satisfied.

Drilling deeper into the poll’s demographics illustrates just how grave the Democrats’ problem is at the moment. Like Donahue, the majority of the self-identified independents surveyed are white, middle-class, middle-aged suburban ticket-splitters — the sort of voters both parties crave.

And when tough economic times are combined with a heavily taxed electorate, as in Massachusetts, the results can be ugly for Democrats.

One Democratic pollster who sampled the state said the tax issue played a pivotal role for Brown in winning over the state’s independents.

“They were worried about taxes more than anything else,” this consultant said. “[Coakley] was seen as a big taxer. [Brown] was seen as someone who wants to lower taxes.”